What is the status of metabolic theory one century after Pütter invented the von Bertalanffy growth curve?

Metabolic theory aims to tackle ecological and evolutionary problems by explicitly including physical principles of energy and mass exchange, thereby increasing generality and deductive power. Individual growth models (IGMs) are the fundamental basis of metabolic theory because they represent the organisational level at which energy and mass exchange processes are most tightly integrated and from which scaling patterns emerge. Unfortunately, IGMs remain a topic of great confusion and controversy about the origins of the ideas, their domain and breadth of application, their logical consistency and whether they can sufficiently capture reality. It is now 100 years since the first theoretical model of individual growth was put forward by Pütter. His insights were deep, but his model ended up being attributed to von Bertalanffy and his ideas largely forgotten. Here I review Pütter's ideas and trace their influence on existing theoretical models for growth and other aspects of metabolism, including those of von Bertalanffy, the Dynamic Energy Budget (DEB) theory, the Gill-Oxygen Limitation Theory (GOLT) and the Ontogenetic Growth Model (OGM). I show that the von Bertalanffy and GOLT models are minor modifications of Pütter's original model. I then synthesise, compare and critique the ideas of the two most-developed theories, DEB theory and the OGM, in relation to Pütter's original ideas. I formulate the Pütter, DEB and OGM models in the same structure and with the same notation to illustrate the major similarities and differences among them. I trace the confusion and controversy regarding these theories to the notions of anabolism, catabolism, assimilation and maintenance, the connections to respiration rate, and the number of parameters and state variables their models require. The OGM model has significant inconsistencies that stem from the interpretation of growth as the difference between anabolism and maintenance, and these issues seriously challenge its ability to incorporate development, reproduction and assimilation. The DEB theory is a direct extension of Pütter's ideas but with growth being the difference between assimilation and maintenance rather than anabolism and catabolism. The DEB theory makes the dynamics of Pütter's ‘nutritive material’ explicit as well as extending the scheme to include reproduction and development. I discuss how these three major theories for individual growth have been used to explain ‘macrometabolic’ patterns including the scaling of respiration, the temperature–size rule (first modelled by Pütter), and the connection to life history. Future research on the connections between theory and data in these macrometabolic topics have the greatest potential to advance the status of metabolic theory and its value for pure and applied problems in ecology and evolution.     

Temperature tolerance and energetics: a dynamic energy budget-based comparison of North Atlantic marine species

Temperature tolerance and sensitivity were examined for some North Atlantic marine species and linked to their energetics in terms of species-specific parameters described by dynamic energy budget (DEB) theory. There was a general lack of basic information on temperature tolerance and sensitivity for many species. Available data indicated that the ranges in tolerable temperatures were positively related to optimal growth temperatures. However, no clear relationships with temperature sensitivity were established and no clear differences between pelagic and demersal species were observed. The analysis was complicated by the fact that for pelagic species, experimental data were completely absent and even for well-studied species, information was incomplete and sometimes contradictory. Nevertheless, differences in life-history strategies were clearly reflected in parameter differences between related species. Two approaches were used in the estimation of DEB parameters: one based on the assumption that reserve hardly contributes to physical volume; the other does not make this assumption, but relies on body-size scaling relationships, using parameter values of a generalized animal as pseudo-data. Temperature tolerance and sensitivity seemed to be linked with the energetics of a species. In terms of growth, relatively high temperature optima, sensitivity and/or tolerance were related to lower relative assimilation rates as well as lower maintenance costs. Making the step from limited observations to underlying mechanisms is complicated and extrapolations should be carefully interpreted. Special attention should be devoted to the estimation of parameters using body-size scaling relationships predicted by the DEB theory.     

恒温和变温下中国对虾生长和能量收支的比较

对比研究了模拟自然昼夜温度变化节律的4个变温(22±2)、(25±2)、(28±2)和(31±2)℃与相应的恒温22、25、28和31℃下中国对虾(F ennerop enaeus ch inensis O sbeck)生长和能量收支的差异。结果表明,对虾在(22±2)℃、(25±2)℃和(28±2)℃变温条件下的生长率显著高于相应的恒温,但(31±2)℃与恒温31℃相比没有显著差异。与相应的恒温相比,(25±2)℃、(28±2)℃和(31±2)℃变温下对虾的摄食量显著增大,(22±2)℃、(25±2)℃和(28±2)℃变温下对虾的饵料转化率则显著提高。但变温下对虾对食物的消化率与相应的恒温相比没有显著差异。能量收支研究结果则发现,(22±2)℃、(25±2)℃和(28±2)℃变温下对虾摄食能中,用于生长的能量比例显著增加,而(31±2)℃与31℃相比则未见显著差异。从而表明,变温促长的主要机制可归因于变温下摄食量的增大、饵料转化率的提高及其摄食能中用于生长能比例的增加。     

Why do hoarding birds gain fat in winter in the wrong way? Suggestions from a dynamic model

In winter, small birds should be fat to avoid starvation andlean and agileto escape predators. This means that they facea trade-off between the costsand benefits of carrying fat reserves.Every day they must gain enough fat tosurvive the coming night.Food-hoarding species can afford to carry less fatthan nonhoardersbecause they can store energy outside the body. Furthermore,hoardersshould avoid carrying excessive fat during the day because theycangain fat fast by retrieving food late in the afternoon.With no storedsupplies, nonhoarders face more unpredictableaccess to food, and they shouldstart gaining fat earlier inthe day. The predicted pattern is then thatnonhoarders gainfat early and that hoarders gain fat late in the day. Recentfielddata show the opposite pattern: hoarders gain relatively morefatreserves in the morning than nonhoarders do. Using a dynamicmodel that mimicsthe conditions in a boreal winter forest,I investigated under whichconditions this pattern will arise.The only assumption of those investigatedthat produced thispattern was to relax the effect of mass-dependent predationrisk.I did this by introducing a limit under which fat reserves didnotaffect predation risk. Hoarders then started the day bygaining fat in themorning. Later, when they had reached a safer(but still not risky) level,they switched to hoarding. Thepattern I searched would only occur if eithernot all food waspossible to store, or if retrieval gave less energy thanforagingin good weather conditions. If I assumed that low levels ofbody fatalso increased predation risk, hoarders would cachein the morning when theycarried least fat. I discuss empiricalevidence for how body fat affectspredation risk. In summary,the factors that produced the pattern I searchedwere a changein the predation-mortality function combined with restrictionsonhoarding.     

Effect of ration and body size on the energy budget of juvenile white sturgeon

Growth and energy budget were measured for three sizes (2.4, 11.1 and 22.5 g) of juvenile white sturgeon Acipenser transmontanus held at 18.5° C and fed tubificid worms at different levels ranging from starvation to ad libitum . For each size-class, specific growth rate increased linearly with increasing ration, and conversion efficiency was highest at the maximum ration. Growth rate decreased with increasing fish size at the maximum ration, but increased with size at each restricted ration. Conversion efficiency increased with increasing ration for each size-class and was usually highest at the maximum ration. Faecal production accounted for 3.2–5.2% of food energy. The proportion of food energy lost in nitrogenous excretion decreased with increasing ration. With increases in ration, the allocation of metabolizable energy to metabolism decreased, while that to growth increased. Fish size had no significant effect on the allocation of metabolizable energy to metabolism or growth. At the maximum ration, on average 64.9% of metabolizable energy was spent on metabolism, and 35.1% on growth.     

Juvenile migration in brown trout: a consequence of energetic state

1. We explored the mechanisms determining age and size at juvenile migration in brown trout Salmo trutta L. A ¹³³Cs tracer methodology was used to estimate food consumption of juvenile brown trout in a Norwegian stream, and the energy budgets of early migrants and stream residents were compared.
2. Fast-growing brown trout migrated to the lake earlier and at a smaller body size than slower-growing individuals. The 2+ migrants were significantly larger than those that remained 1 or more years longer in the stream. The 3+ migrants were significantly larger than the 2+ migrants. Some fast-growing males matured in the stream, whereas all females left the stream before maturing sexually.
3. The food consumption and the energy budgets for 2+ migrants were more than four times higher than those of the resident 2+ fish. Total energy allocated to growth was also higher among migrants, and the total metabolic costs were five times higher among migrants than among resident fish.
4. The proportional energy allocation to growth among the 2+ migrants was much lower (about half) than that of those remaining longer in the stream. The reduction in the proportion of energy available for growth from age 1+ to 2+ was larger among migrants (88%) than among resident fish (68%). Reduction in the proportion of energy available for growth is a probable explanation for why migrations are initiated at age 2.
5. Our study supports the hypothesis that fast-growing individuals shift their niche earlier and at a smaller body size than slower-growing individuals because they maintain higher metabolic rates and are energetically constrained at a younger age by limited food resources than slow growers.     

Effects of temperature on growth and efficiency of food utilization in fifth-instar caterpillars of the tobacco hornworm, Manduca sexta

Fifth-instar larvae of Manduca sexta were reared from hatching on artificial diet at 15, 20, 25, 30 and 35°C. Total development time decreased with increasing temperature. Very few larvae (12%) survived at 15°C, so this temperature was not considered further. There was some mortality at 30°C (11%), and at 35°C (50%).The absolute rate of growth in the fifth instar was faster at 25 than at 20°C, but was similar at 25, 30 and 35°C. This was true both for caterpillars that were chronically exposed to experimental temperatures (i.e. since hatching) and for those acutely exposed (i.e. reared up to fifth instar at 25°C).There was a progressive decrease with higher rearing temperatures in both the initial and final sizes of chronically exposed fifth-instar larvae. Acutely exposed caterpillars matched for initial size showed smaller temperature related differences in final size. Because of these size differences there were differences in relative growth rate which did not reflect true differences in absolute growth rate.Total food consumed by chronically exposed caterpillars was greatest at the lowest temperature (20°C), and decreased progressively with increasing temperature. The absolute rate of food consumption increased from 20 to 25°C, but did not vary significantly between 25 and 35°C. Differences in the sizes of the insects at the different temperatures meant that there were differences among relative measures of consumption that did not reflect absolute food consumption.For chronically exposed caterpillars, none of the three usual indices of food conversion efficiency (AD, ECI and ECD) varied significantly with temperature between 20 and 35°C. This implies that the effects of temperature on metabolic costs are closely matched to food consumption.Oxygen consumption increased with temperature between 20 and 25°C but was temperature compensated between 25 and 35°C.These findings are discussed in terms of their implications for the optimal temperature for growth in Manduca.     

基于logistic模型的中国自然保护区增长动态分析

中国自然保护区建设已由数量扩张型进入质量效益型的新阶段,运用自然保护区统计年鉴数据,基于logistic模型,借助R语言,对自然保护区发展上限进行了估算。同时,运用高等数据曲线曲率求导方法,对发展阶段进行划分,对持续时长和增长速度进行了测算。结果表明:①面积理论饱和值为15470.00万hm²;②将自然保护区发展历程分为缓慢起步期(1956—1989年)、快速发展期(1990—2008年)和稳定完善期(2009—至今);③目前则处于稳定完善期,面积已渐近饱和值,数量仍在小幅度增加。希望本研究结果能为自然保护区主管部门制定管理政策、规划以及整合组建以国家公园为主体的自然保护地体系提供参考。     

Heritability of three condition surrogates in the yellow dung fly

Condition capture has been proposed as a general mechanism maintainingadditive genetic variation, V_a, in sexually selected traitsunder directional selection. It relies on two main assumptions:condition-dependent trait expression and V_a in condition. Althoughthere is evidence for the former, direct evidence that conditionis heritable is scarce, although this is a requirement of mostmodels of handicap sexual selection. We used a parent–offspring,full-sib, two-container laboratory breeding design in the yellowdung fly Scathophaga stercoraria to demonstrate the broad- andnarrow-sense heritability of three surrogates of condition commonlyused in sexual selection studies: lipid and glycogen reserves(i.e., physiological condition), body size, and fluctuatingasymmetry. All three measures are nutrition dependent and havebeen linked to sexual selection in free-living yellow dung flies.While lipid reserves and body size were heritable, asymmetryand glycogen reserves were not. Moreover, the evolvability ofphysiological condition was higher than that of the other twotraits. Of the three surrogates, physiological condition ismost akin to the original definition, but all have their limitations.We conclude that condition is a useful heuristic concept inevolutionary ecology, but its practical value may be limitedby the fact that it cannot be measured directly.     

Modeling the Individual Growth of Tetrahymena Sp. and its Population Consequences

ABSTRACT. Three types of mathematical growth models are presented to describe the individual growth of the ciliate Tetrahymena sp. feeding on the bacterium Pseudomonas fluorescens . Both organisms were isolated from a domestic waste-water treatment plant. Growth of individual ciliates and the consequences for the whole population are considered. Experimental data, obtained by following the individual ciliate during its lifespan from cell division to cell division, are used for parameter estimations. Differences between growth models for individuals turn out to have little effect on the specific population growth rate and the mean cell volume. In case of exponential growth of individuals the unstructured and structured population models are equivalent, even in time-variant environments. This knowledge can be applied in the stability analysis of food chains or forced systems. The results obtained facilitates quantification of protozoa biomass as a function of bacterial biomass in chemostats. More specifically, it highlights the dynamic behaviour of bacteria and protozoa in waste-water treatment plants.     

A general model for effects of temperature on ectotherm ontogenetic growth and development

The temperature size rule (TSR) is the tendency for ectotherms to develop faster but mature at smaller body sizes at higher temperatures. It can be explained by a simple model in which the rate of growth or biomass accumulation and the rate of development have different temperature dependence. The model accounts for both TSR and the less frequently observed reverse-TSR, predicts the fraction of energy allocated to maintenance and synthesis over the course of development, and also predicts that less total energy is expended when developing at warmer temperatures for TSR and vice versa for reverse-TSR. It has important implications for effects of climate change on ectothermic animals.     

Testing mechanistic models of growth in insects

Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg⁻¹) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes.